Landau levels in quasicrystals

Two-dimensional tight-binding models for quasicrystals made of plaquettes with commensurate areas are considered. Their energy spectrum is computed as a function of an applied perpendicular magnetic field. Landau levels are found to emerge near band edges in the zero-field limit. Their existence is related to an effective zero-field dispersion relation valid in the continuum limit. For quasicrystals studied here, an underlying periodic crystal exists and provides a natural interpretation to this dispersion relation. In addition to the slope (effective mass) of Landau levels, we also study their width as a function of the magnetic flux per plaquette and identify two fundamental broadening mechanisms: (i) tunneling between closed cyclotron orbits and (ii) individual energy displacement of states within a Landau level. Interestingly, the typical broadening of the Landau levels is found to behave algebraically with the magnetic field with a nonuniversal exponent.Comment: 14 pages, 9 figure

Geometry of entangled states, Bloch spheres and Hopf fibrations

We discuss a generalization to 2 qubits of the standard Bloch sphere representation for a single qubit, in the framework of Hopf fibrations of high dimensional spheres by lower dimensional spheres. The single qubit Hilbert space is the 3-dimensional sphere S3. The S2 base space of a suitably oriented S3 Hopf fibration is nothing but the Bloch sphere, while the circular fibres represent the qubit overall phase degree of freedom. For the two qubits case, the Hilbert space is a 7-dimensional sphere S7, which also allows for a Hopf fibration, with S3 fibres and a S4 base. A main striking result is that suitably oriented S7 Hopf fibrations are entanglement sensitive. The relation with the standard Schmidt decomposition is also discussedComment: submitted to J. Phys.

Adiabatic Computation - A Toy Model

We discuss a toy model for adiabatic quantum computation which displays some phenomenological properties expected in more realistic implementations. This model has two free parameters: the adiabatic evolution parameter $s$ and the $\alpha$ parameter which emulates many-variables constrains in the classical computational problem. The proposed model presents, in the $s-\alpha$ plane, a line of first order quantum phase transition that ends at a second order point. The relation between computation complexity and the occurrence of quantum phase transitions is discussed. We analyze the behavior of the ground and first excited states near the quantum phase transition, the gap and the entanglement content of the ground state.Comment: 7 pages, 8 figure

Entanglement in a first-order quantum phase transition

4 págs.; 3 figs.; PACS number(s): 03.65.Ud, 03.67.Mn, 73.43.NqThe entanglement properties of the ground state for a system of spins half embedded in a magnetic field were investigated. A first-order transition was obtained at zero field. It was found that two-spin entanglement displays a jump at the transition point. It was shown that the symmetries of the Hamiltonian allow to simplify the diagnolization.Peer Reviewe

Tunable Aharonov-Bohm-like cages for quantum walks

Aharonov-Bohm cages correspond to an extreme confinement for two-dimensional tight-binding electrons in a transverse magnetic field. When the dimensionless magnetic flux per plaquette $f$ equals a critical value $f_c=1/2$, a destructive interference forbids the particle to diffuse away from a small cluster. The corresponding energy levels pinch into a set of highly degenerate discrete levels as $f\to f_c$. We show here that cages also occur for discrete-time quantum walks on either the diamond chain or the $\mathcal{T}_3$ tiling but require specific coin operators. The corresponding quasi-energies versus $f$ result in a Floquet-Hofstadter butterfly displaying pinching near a critical flux $f_c$ and that may be tuned away from 1/2. The spatial extension of the associated cages can also be engineered.Comment: 9 pages, 9 figure

Geometric study of a 2D tiling related to the octagonal quasiperiodic tiling

International audienceA quasicrystal built with three types of tiles is related to the well-known octagonal tiling. The relationships between both tilings are investigated. More precisely, we show that the coordinates of the vertices can be obtained in two different but equivalent ways. The structure factor is calculated exactly. We emphasize the difficulty one can have to define the order of the symmetry of a quasicrystal, from a practical point of view, exhibiting a quasiperiodic tiling whose spectrum has a « quasi » eight-fold symmetry. Finally, we show how to recover easily a class of octagonal-like quasicrystals.Au moyen de trois tuiles, nous construisons un pavage quasipériodique du plan, que nous relions au quasicristal octogonal. Ainsi, nous montrons que les coordonnées des nœuds peuvent être obtenues de deux manières différentes. Le facteur de structure est calculé exactement. Ce pavage qui possède « presque » une symétrie d'ordre huit, soulève la difficulté de la détermination pratique de la symétrie d'un quasicristal. Finalement, nous montrons comment construire une large classe de pavage du type de l'octogonal, à partir de ce nouveau pavage

Meta-Analysis of a Complex Network of Non-Pharmacological Interventions: The Example of Femoral Neck Fracture

Background Surgical interventions raise specific methodological issues in network meta-analysis (NMA). They are usually multi-component interventions resulting in complex networks of randomized controlled trials (RCTs), with multiple groups and sparse connections. Purpose To illustrate the applicability of the NMA in a complex network of surgical interventions and to prioritize the available interventions according to a clinically relevant outcome. Methods We considered RCTs of treatments for femoral neck fracture in adults. We searched CENTRAL, MEDLINE, EMBASE and ClinicalTrials.gov up to November 2015. Two reviewers independently selected trials, extracted data and used the Cochrane Collaboration’s tool for assessing the risk of bias. A group of orthopedic surgeons grouped similar but not identical interventions under the same node. We synthesized the network using a Bayesian network meta-analysis model. We derived posterior odds ratios (ORs) and 95% credible intervals (95% CrIs) for all possible pairwise comparisons. The primary outcome was all-cause revision surgery. Results Data from 27 trials were combined, for 4,186 participants (72% women, mean age 80 years, 95% displaced fractures). The median follow-up was 2 years. With hemiarthroplasty (HA) and total hip arthroplasty (THA) as a comparison, risk of surgical revision was significantly higher with the treatments unthreaded cervical osteosynthesis (OR 8.0 [95% CrI 3.6–15.5] and 5.9 [2.4–12.0], respectively), screw (9.4 [6.0–16.5] and 6.7 [3.9–13.6]) and plate (12.5 [5.8–23.8] and 7.8 [3.8–19.4]). Conclusions In older women with displaced femoral neck fractures, arthroplasty (HA and THA) is the most effective treatment in terms of risk of revision surgery